Finite Group Databasebeta

← C2×#21461201 #30610913

Subgroups — C2×#21461201 #30610913

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840780C211yesmaximal, characteristic
2C2×C4×C4⋊#6923C211yesmaximal, characteristic
3#21461201C218yesmaximal, direct product factor
4C2×#16840616C212yesmaximal
5C2×#16840615C212yesmaximal
6C2×#16840316C211yesmaximal, characteristic
7C22×C4⋊#6923—21no—
8C22×C4×#6923—21no—
9#16840780—22no—
10#16840780C2214yes—
11C2×#14519844—21no—
12C2×#14519834C2212yes—
13C2×C4×#92420—21no—
14C4×C4⋊#6923—22no—
15C4×C4⋊#6923C2214yes—
16C2×(C2×#6923)⋊C4C2212yes—
17#16840616C2218yes—
18#16840615C2218yes—
19#16840316—22no—
20#16840316—22no—
21#16840316C414yescomplemented
22#16840316C2214yes—
23C2×#14519776C411yescharacteristic, complemented
24C2×#14519775C411yescharacteristic, complemented
25C2×#14519767—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519755—21no—
28C2×#14519753C2211yescharacteristic
29C2×C4×Dic122—21no—
30C2×C4×Dic122C411yescharacteristic, complemented
31C2×#14519734—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×Q8×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C22×#92420—22no—
36C2×C4⋊#6923—28no—
37C2×C4⋊#6923—24no—
38C2×C4×#6923—24no—
39C2×C4×#6923—44no—
40#14519844—24no—
41#14519834—22no—
42#14519834C2314yes—
43C4×#92420—24no—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4C2314yes—
46C22×Dic122—21no—
47C22×Dic122C2×C411yescharacteristic
48C22×C4×D61D411yescharacteristic
49C22×C4×D61D411yescharacteristic
50C22×C4×D61C2311yescharacteristic
51#14519776—22no—
52#14519776C2×C414yescomplemented
53#14519775—22no—
54#14519775C2×C414yescomplemented
55#14519767—24no—
56#14519767—24no—
57#14519757—21no—
58#14519757—21no—
59#14519757C2×C412yes—
60#14519757C2312yes—
61#14519755—24no—
62#14519755—24no—
63#14519753—21no—
64#14519753—21no—
65#14519753C2×C412yes—
66#14519753C2312yes—
67C4×Dic122—22no—
68C4×Dic122—24no—
69C4×Dic122—24no—
70C4×Dic122C2×C414yescomplemented
71#14519734—24no—
72#14519734—24no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D411yescharacteristic
86C42×D61C2×C412yes—
87C42×D61D412yes—
88C42×D61D412yes—
89C42×D61C2312yes—
90C22×Q8×C61C2×C411yescharacteristic
91C4×Q8×C61—22no—
92C4×Q8×C61C2×C414yescomplemented
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61—21no—
96C2×C42×C61C2×C411yescharacteristic
97C23×D61C2×D411yescharacteristic
98C22×#6923—28no—
99C22×#6923—24no—
100C22×#6923—44no—
101C22×#6923—44no—
102C2×Q8×C61—21no—
103C2×Q8×C61—42no—
104C2×Q8×C61C22×C412yes—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C22⋊C411yescharacteristic
109C22×C4×C61C22×C411yescharacteristic
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C2×D411yescharacteristic
115C2×C4×D61—24no—
116C2×C4×D61—42no—
117C2×C4×D61C22⋊C412yes—
118C2×C4×D61C22⋊C412yes—
119C2×C4×D61SD1614yes—
120C2×C4×D61Q1614yes—
121C2×C4×D61C22×C411yescharacteristic
122C2×C4×D61C2×D412yes—
123C2×C4×D61C2×D411yescharacteristic
124C2×C4×D61C2×D411yescharacteristic
125C2×C4×D61C2×D412yes—
126C2×C4×D61C2411yescharacteristic
127C2×Dic122—21no—
128C2×Dic122—24no—
129C2×Dic122—44no—
130C2×Dic122—42no—
131C2×Dic122C22×C412yes—
132C2×#92420—24no—
133C2×#92420—44no—
134C4⋊#6923—216no—
135C4×#6923—48no—
136C4⋊C4×C61—24no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61C22×C412yes—
139C42×C61—24no—
140C42×C61C22⋊C412yes—
141C42×C61C22×C412yes—
142#11758198—22no—
143#11758198—22no—
144#11758198—22no—
145#11758198—22no—
146C4⋊Dic61—21no—
147C4⋊Dic61—22no—
148C4⋊Dic61—22no—
149C4⋊Dic61C22×C412yes—
150#11758196—24no—
151#11758196—24no—
152#11758196—24no—
153#11758196—22no—
154#11758196—24no—
155#11758196—22no—
156C4×Dic61—24no—
157C4×Dic61C22⋊C412yes—
158C4×Dic61C22⋊C412yes—
159C4×Dic61C22⋊C412yes—
160C4×Dic61C22×C412yes—
161C4×Dic61C2×D412yes—
162C4×Dic61C2×D412yes—
163C23×C61C2×C22⋊C411yescharacteristic
164C22×D61—22no—
165C22×D61—22no—
166C22×D61C2×C22⋊C411yescharacteristic
167C22×D61C2×SD1612yes—
168C22×D61C2×Q1612yes—
169C22×D61C22×D411yescharacteristic
170C2×#6923—28no—
171C2×#6923—44no—
172C2×#6923—416no—
173C2×#6923—44no—
174Q8×C61—42no—
175Q8×C61—42no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61#10314yes—
183C2×C4×C61C2×C22⋊C411yescharacteristic
184C2×C4×C61C2×C22⋊C412yes—
185C2×C4×C61C2×C22⋊C412yes—
186C2×C4×C61C23×C411yescharacteristic
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61#10314yes—
193C2×Dic61#10414yes—
194C2×Dic61C2×C22⋊C411yescharacteristic
195C2×Dic61C2×C22⋊C412yes—
196C2×Dic61C2×C22⋊C412yes—
197C2×Dic61C22×D411yescharacteristic
198C4×D61—24no—
199C4×D61—24no—
200C4×D61—41no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61#10318yes—
205C4×D61C2×SD1614yes—
206C4×D61C2×Q1614yes—
207Dic122—42no—
208Dic122—48no—
209Dic122—42no—
210#92420—44no—
211C2×#1503—611nomaximal, Sylow
212C22×C61#41012yes—
213C22×C61C2×#10312yes—
214C22×C61C2×#10412yes—
215C22×C61C22×C22⋊C411yescharacteristic
216C2×D61—21no—
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—24no—
221C2×D61—24no—
222C2×D61C2×#10312yes—
223C2×D61C22×SD1611yescharacteristic
224C2×D61C22×Q1611yescharacteristic
225#6923—48no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—22no—
229C4×C61—42no—
230C4×C61—42no—
231C4×C61C2×#10314yes—
232Dic61—21no—
233Dic61—21no—
234Dic61—42no—
235Dic61—42no—
236Dic61C2×#10314yes—
237Dic61C2×#10414yes—
238C2×#533—611no—
239C2×#431—611no—
240C2×C4×C4⋊C4—611no—
241#1503—618no—
242C2×#328—612no—
243C2×#328—612no—
244C2×C61#150314yescomplemented
245C2×C61C2×#41011yescharacteristic
246C2×C61C22×#10311yescharacteristic
247C2×C61C22×#10411yescharacteristic
248D61—21no—
249D61—21no—
250D61—22no—
251#533—614no—
252#533—614no—
253#533—1222no—
254#533—1222no—
255C2×C4⋊Q8—611no—
256C2×C4⋊Q8—611no—
257C2×#125—1221no—
258C2×C22⋊Q8—611no—
259C2×C22⋊Q8—611no—
260C2×C22⋊Q8—1221no—
261C2×C4×Q8—611no—
262C2×C4×Q8—1221no—
263C2×C4×Q8#692311yescharacteristic, complemented
264C2×#117—1221no—
265C22×C4⋊C4—1221no—
266C22×C42—611no—
267C22×C42—1221no—
268#431—614no—
269#431—1222no—
270C2×C4⋊C8—1221no—
271C2×C22⋊C8—612no—
272C2×C4×C8—1221no—
273C4×C4⋊C4—614no—
274C4×C4⋊C4—1222no—
275C2×#95—612no—
276#328—618no—
277#328—618no—
278C61C2×#150311yescharacteristic, complemented, Sylow
279C22×Q8—611no—
280C22×Q8—1221no—
281C22×Q8C2×#692311yescharacteristic
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—1222no—
286C22×C8—1222no—
287C4⋊Q8—614no—
288C4⋊Q8—614no—
289C4⋊Q8—1222no—
290C4⋊Q8—1222no—
291#125—1224no—
292#125—1224no—
293C22⋊Q8—612no—
294C22⋊Q8—612no—
295C22⋊Q8—612no—
296C22⋊Q8—612no—
297C22⋊Q8—1221no—
298C22⋊Q8—1221no—
299C22⋊Q8—1224no—
300C22⋊Q8—1224no—
301C22⋊Q8—1221no—
302C22⋊Q8—1221no—
303C4×Q8—22no—
304C4×Q8—614no—
305C4×Q8—1224no—
306C4×Q8—1224no—
307C4×Q8—1222no—
308C4×Q8C2×#692314yescomplemented
309#117—1224no—
310#117—1224no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—611no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1224no—
319C2×C4⋊C4—1228no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4C2×#692311yescharacteristic
322C2×C22⋊C4—1221no—
323C2×C22⋊C4—1221no—
324C2×C42—21no—
325C2×C42—611no—
326C2×C42—611no—
327C2×C42—611no—
328C2×C42—612no—
329C2×C42—612no—
330C2×C42—612no—
331C2×C42—612no—
332C2×C42—1221no—
333C2×C42—1224no—
334C2×C42—2444no—
335C2×C42C2×#692311yescharacteristic
336C4⋊C8—1224no—
337C22⋊C8—614no—
338C22⋊C8—1222no—
339C4×C8—1224no—
340#95—614no—
341#95—1222no—
342C24—611no—
343C2×Q8—21no—
344C2×Q8—42no—
345C2×Q8—612no—
346C2×Q8—1224no—
347C2×Q8—1221no—
348C2×Q8—2442no—
349C2×Q8—2444no—
350C2×Q8C22×#692312yes—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—614no—
356C22×C4—614no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—611no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—1224no—
367C22×C4—1224no—
368C22×C4—1228no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—2442no—
372C22×C4—2444no—
373C22×C4—2444no—
374C22×C4C22⋊#692311yescharacteristic
375C22×C4C22⋊#692311yescharacteristic
376C22×C4C22×#692311yescharacteristic
377C2×C8—1224no—
378C2×C8—2444no—
379C4⋊C4—24no—
380C4⋊C4—21no—
381C4⋊C4—612no—
382C4⋊C4—1224no—
383C4⋊C4—1224no—
384C4⋊C4—1222no—
385C4⋊C4—1222no—
386C4⋊C4—1224no—
387C4⋊C4—1222no—
388C4⋊C4—1222no—
389C4⋊C4—12216no—
390C4⋊C4—1221no—
391C4⋊C4—1224no—
392C4⋊C4C22×#692312yes—
393C22⋊C4—1222no—
394C22⋊C4—1222no—
395C22⋊C4—1222no—
396C22⋊C4—1222no—
397C42—24no—
398C42—612no—
399C42—612no—
400C42—612no—
401C42—612no—
402C42—612no—
403C42—612no—
404C42—1224no—
405C42—2448no—
406C42C22⋊#692312yes—
407C42C22×#692312yes—
408C23—612no—
409C23—612no—
410C23—611no—
411C23—611no—
412C23—1222no—
413C23—1222no—
414C23C2×C22⋊#692311yescharacteristic
415Q8—42no—
416Q8—42no—
417Q8—2442no—
418Q8—2442no—
419Q8—2448no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—614no—
427C2×C4—614no—
428C2×C4—612no—
429C2×C4—612no—
430C2×C4—618no—
431C2×C4—614no—
432C2×C4—614no—
433C2×C4—611no—
434C2×C4—611no—
435C2×C4—1224no—
436C2×C4—1224no—
437C2×C4—1222no—
438C2×C4—1228no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2444no—
446C2×C4—2444no—
447C2×C4—24416no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4#1451984014yes—
451C2×C4C2×C22⋊#692311yescharacteristic
452C2×C4C2×C22⋊#692312yes—
453C2×C4C2×C22⋊#692312yes—
454C2×C4C23×#692311yescharacteristic
455C8—2444no—
456C22—611no—
457C22—611no—
458C22—612no—
459C22—1221no—
460C22—1221no—
461C22—1221no—
462C22—1221no—
463C22—1224no—
464C22—1224no—
465C22#1684074112yes—
466C22C2×#1451984012yes—
467C22D61⋊#10412yes—
468C22C22×C22⋊#692311yescharacteristic
469C4—21no—
470C4—21no—
471C4—22no—
472C4—42no—
473C4—42no—
474C4—614no—
475C4—614no—
476C4—1221no—
477C4—1221no—
478C4—2448no—
479C4—2442no—
480C4—2442no—
481C4C2×#1451984014yes—
482C2—1221no—
483C2—1221no—
484C2—1222no—
485C2#2146120114yesdirect product factor
486C2C2×#1684074111yescharacteristic
487C2C22×#1451984011yescharacteristic
488C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1503
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21461201C2direct (N × H)
21. #16840316C4semidirect
23. C2×#14519776C4semidirect
24. C2×#14519775C4semidirect
30. C2×C4×Dic122C4semidirect
33. C2×C4×Q8×C61C4semidirect
52. #14519776C2×C4semidirect
54. #14519775C2×C4semidirect
70. C4×Dic122C2×C4semidirect
92. C4×Q8×C61C2×C4semidirect
244. C2×C61#1503semidirect
263. C2×C4×Q8#6923semidirect
278. C61C2×#1503semidirect
308. C4×Q8C2×#6923semidirect
485. C2#21461201direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168407802
C2×C4×C4⋊#69232
#214612012
C2×#168406162
C2×#168406152
C2×#168403162
C2×#150361